Template Numerical Library version develop:1f26cbe9a
TNL::Solvers::Linear Namespace Reference

Namespace for linear system solvers. More...

## Namespaces

namespace  Preconditioners
Namespace for preconditioners of linear system solvers.

## Classes

class  BICGStab
Iterative solver of linear systems based on the biconjugate gradient stabilized (BICGStab) method. More...

class  BICGStabL
Iterative solver of linear systems based on the BICGStab(l) method. More...

class  CG
Iterative solver of linear systems based on the conjugate gradient method. More...

class  GMRES
Iterative solver of linear systems based on the Generalized minimal residual (GMRES) method. More...

class  Jacobi
Iterative solver of linear systems based on the Jacobi method. More...

struct  LinearResidueGetter

class  LinearSolver
Base class for iterative solvers of systems of linear equations. More...

class  SOR
Iterative solver of linear systems based on the Successive-overrelaxation (SOR) or Gauss-Seidel method. More...

class  TFQMR
Iterative solver of linear systems based on the Transpose-free quasi-minimal residual (TFQMR) method. More...

struct  Traits

struct  Traits< Matrices::DistributedMatrix< Matrix > >

## Functions

template<bool fullStorage = true, typename Matrix , typename Vector1 , typename Vector2 >
void triangularSolveLower (const Matrix &L, Vector1 &x, const Vector2 &b)

template<bool reversedRows = false, bool fullStorage = true, typename Matrix , typename Vector1 , typename Vector2 >
void triangularSolveUpper (const Matrix &U, Vector1 &x, const Vector2 &b)

## Detailed Description

Namespace for linear system solvers.

This namespace contains the following algorithms and methods for solution of linear systems.

# Iterative methods

## Stationary methods

1. Jacobi method - TNL::Solvers::Linear::Jacobi
2. Successive-overrelaxation method, SOR - TNL::Solvers::Linear::SOR

## Krylov subspace methods

1. Conjugate gradient method, CG - TNL::Solvers::Linear::CG
2. Biconjugate gradient stabilized method, BICGStab - TNL::Solvers::Linear::BICGStab
3. BICGStab(l) method - TNL::Solvers::Linear::BICGStabL
4. Transpose-free quasi-minimal residual method, TFQMR - TNL::Solvers::Linear::TFQMR
5. Generalized minimal residual method, GMERS - TNL::Solvers::Linear::GMRES with various methods of orthogonalization
1. Classical Gramm-Schmidt, CGS
2. Classical Gramm-Schmidt with reorthogonalization, CGSR
3. Modified Gramm-Schmidt, MGS
4. Modified Gramm-Schmidt with reorthogonalization, MGSR
5. Compact WY form of the Householder reflections, CWY